Geodesics and Submanifold Structures in Conformal Geometry

الأصل · EN

A conformal structure on a manifold Mⁿ induces natural second order conformally invariant operators, called Möbius and Laplace structures, acting on specific weight bundles of M, provided that n≥ 3. By extending the notions of Möbius and Laplace structures to the case of surfaces and curves, we develop here the theory of extrinsic conformal geometry for submanifolds, find tensorial invariants of a conformal embedding, and use these invariants to characterize various forms of geodesic submanifolds.